Buckle, who was 37 on Sunday, refused to confirm or deny the talks, and chief executive Colin Lee declined to comment ahead of a formal announcement.
But United want to tie up the new agreement before they head into a Christmas/New Year programme which includes two local derbies against Buckle's old club Exeter City.
There has been some speculation that one or two League Two clubs might be interested in trying to lure Buckle, who moved from Exeter to take over United six months ago, away from Plainmoor.
But I understand that he is committed to the business of trying to lead United to promotion this season.
And the club is planning for a longer-term future of which Buckle is very much an important part.
Source: http://www.thisissouthdevon.co.uk./